{
  "id": "0809.1546",
  "version": "v1",
  "published": "2008-09-09T14:47:46.000Z",
  "updated": "2008-09-09T14:47:46.000Z",
  "title": "On the Equicontinuity Region of Discrete Subgroups of PU(1,n)",
  "authors": [
    "José Seade",
    "Angel Cano"
  ],
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $ G $ be a discrete subgroup of PU(1,n). Then $ G $ acts on $\\mathbb {P}^n_\\mathbb C$ preserving the unit ball $\\mathbb {H}^n_\\mathbb {C}$, where it acts by isometries with respect to the Bergman metric. In this work we determine the equicontinuty region $Eq(G)$ of $G$ in $\\mathbb P^n_{\\mathbb C}$: It is the complement of the union of all complex projective hyperplanes in $\\mathbb {P}^n_{\\mathbb C}$ which are tangent to $\\partial \\mathbb {H}^n_\\mathbb {C}$ at points in the Chen-Greenberg limit set $\\Lambda_{CG}(G )$, a closed $G$-invariant subset of $\\partial \\mathbb {H}^n_\\mathbb {C}$, which is minimal for non-elementary groups. We also prove that the action on $Eq(G)$ is discontinuous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-09T14:47:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q45",
      "37F45",
      "22E40",
      "57R30"
    ],
    "keywords": [
      "discrete subgroup",
      "equicontinuity region",
      "chen-greenberg limit set",
      "non-elementary groups",
      "equicontinuty region"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.1546S"
    }
  }
}